Digital Audio is based on many different means of communication. The different digital media generally have conflicting sampling frequencies, where those sampling frequencies are in accordance with the Nyquist Sampling theorem. For example, digital transmission of broadcasting programs at 32 kHz, compact discs at 44.1 kHz, digital video discs at 48 kHz and speech recordings at 6 kHz to 8 kHz, as described in “High Quality Digital Audio in the Entertainment Industry”, IEEE ASSP Magazine 1985 pages 2–25. Digital audio requires a sampling frequency conversion technique to handle simple as well as non-trivial ratios efficiently.
Conversion by going from digital to analogue (through a DAC and a low-pass filter) and then re-sampling the smoothed signal at the output rate is simple, but costly and limited by the imperfections (non-linearity, phase response, noise) of the analogue filter as described in “High, Quality Analogue Filters for Digital Audio”, 67th AES Convention, November 1980.
Conversion in simple integer or rational ratios fi/f0 by single or multi-stage FIR filter design, as described in Rabiner and Croichie, Multi-rate Digital Signal Processing, Prentice Hall Publication, 1983. However, it is not particularly suited for many arbitrary ratios, as it leads to far too many filter configurations. An individual filter configuration is suited maximally to a subset of these ratios only.